unitary representation
continuous group homomorphism from some topological group to the topological group of unitary transformations on a Hilbert space
discrete series representation
irreducible unitary subrepresentation of the left regular representation of a locally compact group on square-integrable functions
theta representation
unitary representation of the real Heisenberg group on a Hilbert space of holomorphic functions, such that the only fixed points of the action of the integer Heisenberg group are (scalar multiples of) the Jacobi theta function